 mersenneforum.org > Math I get 13% less primes than I expected:-(
 Register FAQ Search Today's Posts Mark Forums Read 2010-10-29, 16:47 #1 mart_r   Dec 2008 you know...around... 2×353 Posts I get 13% less primes than I expected:-( Suppose I have an integer of magnitude of about 1028. If this number has no factors less than 104, am I right in assuming that this leaves a chance of about log(1028)/(2*log(104)) = 1:3.5, i.e. 28.57%, that this number will be prime?   2010-10-29, 17:17   #2
axn

Jun 2003

34×5×13 Posts Quote:
 Originally Posted by mart_r Suppose I have an integer of magnitude of about 1028. If this number has no factors less than 104, am I right in assuming that this leaves a chance of about log(1028)/(2*log(104)) = 1:3.5, i.e. 28.57%, that this number will be prime?
By Merten's theorem, log(1028)/(1.781*log(104)) is a better approximation.

1.781 =e^gamma   2010-10-29, 17:31   #3
mart_r

Dec 2008
you know...around...

10110000102 Posts Quote:
 Originally Posted by axn By Merten's theorem, log(1028)/(1.781*log(104)) is a better approximation. 1.781 =e^gamma
Oh! That would explain everything.
Thanks!  Thread Tools Show Printable Version Email this Page Similar Threads Thread Thread Starter Forum Replies Last Post CRGreathouse PrimeNet 2 2018-01-10 06:13 Batalov Computer Science & Computational Number Theory 5 2016-08-11 01:17 ewmayer Probability & Probabilistic Number Theory 6 2015-11-10 16:33 gd_barnes Riesel Prime Search 15 2010-10-14 22:00 robert44444uk Math 18 2008-04-02 21:19

All times are UTC. The time now is 07:48.

Thu Jan 20 07:48:33 UTC 2022 up 181 days, 2:17, 0 users, load averages: 1.20, 1.22, 1.20